Here : "she wants her stopping distance" << this is d "not to exceed 240ft", that is d<240.
So you have to find v such that d = v + vē/20 < 240.
Think "quadratic" !
Advice : be careful, speed is in mi/h and distance in ft in the formula. So don't bother changing the units to be the same or wondering about them your result will automatically be in mi/h.
Edit : woah... 28th post